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vichka [17]
2 years ago
9

You want to to buy the PlayStation 5 and it is listed as $449.99 in all the stores

Mathematics
1 answer:
Anna71 [15]2 years ago
7 0

Answer:

Without taxes, the price will be $359.99

Step-by-step explanation:

You take the original price then divide it by ten. Then you multiply that number by 2 to get what 20% of 449.99 is. You then subtract that number from from 449.99. At least I think so. There are other ways to go faster but this is the easiest to understand.

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Which shape goes in the empty box in order to complete nathans mobile
Harman [31]

Step-by-step explanation:

yes

4 0
3 years ago
4. Diego is thinking of two positive numbers. He says, "If we triple the first number and
aleksandr82 [10.1K]

Answer:

3<em>x </em>+ 2<em>y</em> = 34. and two possible pairs of positive numbers are  (<em>x</em>, <em>y</em>) = (10, 2) and (<em>x</em>, <em>y</em>) = (4, 11).

Step-by-step explanation:

 Let the First positive number be <em>x</em> and second positive number be <em>y.</em>

Triple of first number = 3<em>x</em>

double of second number = 2<em>y</em>

According to question,

3<em>x </em>+ 2<em>y</em> = 34

Therefore, the equation is 3<em>x </em>+ 2<em>y</em> = 34

So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3<em>x </em>+ 2<em>y</em> = 34

Now,  3<em>x </em>+ 2<em>y</em> = 34

3<em>x </em>= 34 - 2<em>y</em>

Let x = 10 and by substituting its value in above expression,

3 \times 10 = 34 - 2y

30 = 34 - 2y

2y = 34 - 30

2y = 4

y = 2

Therefore first pair (<em>x</em>, <em>y</em>) = (10, 2)

In the same way put x = 4 then,

3<em>x </em>= 34 - 2<em>y</em>

3 \times 4 = 34 - 2y

2y = 34 - 12

2y = 22

y = 11

Therefore first pair (<em>x</em>, <em>y</em>) = (4, 11)

Therefore, (<em>x</em>, <em>y</em>) = (4, 11) and  (<em>x</em>, <em>y</em>) = (10, 2) are the two possible pairs of numbers Diego could be thinking of as these both values satisfy the equation 3<em>x </em>+ 2<em>y</em> = 34.  

8 0
2 years ago
5x minus 4 equals x squared minus 4x plus 4. What is x
Sauron [17]

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((0 -  5x2) -  4x) -  4  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  -5x2 - 4x - 4  =   -1 • (5x2 + 4x + 4)

Trying to factor by splitting the middle term

3.2     Factoring  5x2 + 4x + 4

The first term is,  5x2  its coefficient is  5 .

The middle term is,  +4x  its coefficient is  4 .

The last term, "the constant", is  +4

Step-1 : Multiply the coefficient of the first term by the constant   5 • 4 = 20

Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   4 .

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 -5x2 - 4x - 4  = 0

Step  4  :

Parabola, Finding the Vertex :

4.1      Find the Vertex of   y = -5x2-4x-4

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.4000  

Plugging into the parabola formula  -0.4000  for  x  we can calculate the  y -coordinate :

 y = -5.0 * -0.40 * -0.40 - 4.0 * -0.40 - 4.0

or   y = -3.200

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -5x2-4x-4

Axis of Symmetry (dashed)  {x}={-0.40}

Vertex at  {x,y} = {-0.40,-3.20}

Function has no real roots

Solve Quadratic Equation by Completing The Square

4.2     Solving   -5x2-4x-4 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

5x2+4x+4 = 0  Divide both sides of the equation by  5  to have 1 as the coefficient of the first term :

  x2+(4/5)x+(4/5) = 0

Subtract  4/5  from both side of the equation :

  x2+(4/5)x = -4/5

Add  4/25  to both sides of the equation :

 On the right hand side we have :

  -4/5  +  4/25   The common denominator of the two fractions is  25   Adding  (-20/25)+(4/25)  gives  -16/25

 So adding to both sides we finally get :

  x2+(4/5)x+(4/25) = -16/25

Adding  4/25  has completed the left hand side into a perfect square :

  x2+(4/5)x+(4/25)  =

  (x+(2/5)) • (x+(2/5))  =

 (x+(2/5))2

Things which are equal to the same thing are also equal to one another. Since

  x2+(4/5)x+(4/25) = -16/25 and

  x2+(4/5)x+(4/25) = (x+(2/5))2

then, according to the law of transitivity,

  (x+(2/5))2 = -16/25

Note that the square root of

  (x+(2/5))2   is

  (x+(2/5))2/2 =

 (x+(2/5))1 =

  x+(2/5)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(2/5) = √ -16/25

Subtract  2/5  from both sides to obtain:

  x = -2/5 + √ -16/25

Since a square root has two values, one positive and the other negative

  x2 + (4/5)x + (4/5) = 0

  has two solutions:

 x = -2/5 + √ 16/25 •  i

  or

 x = -2/5 - √ 16/25 •  i

Note that  √ 16/25 can be written as

 √ 16  / √ 25   which is 4 / 5

Solve Quadratic Equation using the Quadratic Formula

4.3     Solving    -5x2-4x-4 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                   

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     -5

                     B   =    -4

                     C   =   -4

Accordingly,  B2  -  4AC   =

                    16 - 80 =

                    -64

Applying the quadratic formula :

              4 ± √ -64

  x  =    —————

                   -10

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -64  =

                   √ 64 • (-1)  =

                   √ 64  • √ -1   =

                   ±  √ 64  • i

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is

  2•2•2•2•2•2

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =

               ±  8 • √ 1   =

               ±  8

So now we are looking at:

          x  =  ( 4 ± 8i ) / -10

Two imaginary solutions :

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

 or:

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

<em>hope i helped</em>

<em>-Rin:)</em>

6 0
3 years ago
Read 2 more answers
-5(c-4)=<br> a*-20-5c<br> b*20-5c<br> c*20+5c<br> ???????
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Answer:

b

Step-by-step explanation:

distributive property-

-5c-(-20) which is -5c+20 which can also be 20-5c

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Step-by-step explanation:

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